runge_kutta_semiimplicit.icc
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namespace rk {
// see WanShuZha-2015 page 212
constexpr size_t pmax = 3;
const Float _g2 = 1 - 1/sqrt(Float(2));
const Float _d2 = 1 - 1/(2*_g2);
const Float _g3 = 0.435866521508459;
const Float _b31 = -3*(_g3*_g3)/2 + 4*_g3 - 1./4;
const Float _b32 = 3*(_g3*_g3)/2 - 5*_g3 + 5./4;
const Float _a31 = -0.356;
const Float _a32 = (1/Float(3) - 2*(_g3*_g3) - 2*_b32*_a31*_g3)/(_g3*(1-_g3));
Float alpha[][pmax+1][pmax+1]
= { {},
{ {0},
{0, 1} },
{ {0},
{0, _g2},
{0, 1-_g2, _g2} },
{ {0},
{0, _g3},
{0, (1-_g3)/2, _g3},
{0, _b31, _b32, _g3} } };
Float tilde_alpha[][pmax+1][pmax+1]
= { {},
{ {},
{1} },
{ {},
{_g2},
{_d2, 1-_d2} },
{ {},
{_g3},
{(1+_g3)/2 - _a31, _a31},
{0, 1-_a32, _a32} } };
Float beta [][pmax+1]
= { {},
{0, 1},
{0, 1-_g2, _g2},
{0, _b31, _b32, _g3} };
Float tilde_beta [][pmax+1]
= { {},
{1},
{_d2, 1-_d2, 0},
{0, _b31, _b32, _g3} };
Float gamma [][pmax+1]
= { {},
{0, 1},
{0, _g2, 1},
{0, _g3, (1+_g3)/2, 1} };
} // namespace rk
Float
see the Float page for the full documentation
rk
Definition: runge_kutta_semiimplicit.icc:25
rk::_b32
const Float _b32
Definition: runge_kutta_semiimplicit.icc:32
rk::tilde_alpha
Float tilde_alpha[][pmax+1][pmax+1]
Definition: runge_kutta_semiimplicit.icc:48
rk::_d2
const Float _d2
Definition: runge_kutta_semiimplicit.icc:29
rk::_g3
const Float _g3
Definition: runge_kutta_semiimplicit.icc:30
rk::_a31
const Float _a31
Definition: runge_kutta_semiimplicit.icc:33
rk::tilde_beta
Float tilde_beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:65
rk::_b31
const Float _b31
Definition: runge_kutta_semiimplicit.icc:31
rk::gamma
Float gamma[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:70
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60
rk::alpha
Float alpha[][pmax+1][pmax+1]
Definition: runge_kutta_semiimplicit.icc:36
rk::_a32
const Float _a32
Definition: runge_kutta_semiimplicit.icc:34
rk::pmax
constexpr size_t pmax
Definition: runge_kutta_semiimplicit.icc:27
rk::_g2
const Float _g2
Definition: runge_kutta_semiimplicit.icc:28